The noun resolution has a few related meanings having to do with being firmly determined about something. If you lack determination, you'll never fulfill your New Year's resolutions.
Resolution is the noun form of the verb resolve, derived from the Latin resolvere, "to loosen, undo, settle." We can still see this meaning of resolution in the sense of "an explanation" or "a solution" — when a problem, conflict, or mystery reaches its resolution, it has been "undone," so to speak. If you approach a task with resolution, you do it with determination. And if you make a resolution, you make a firm decision to do something or meet some goal.